The automatic and destruction-free testing of objects or components by means of X-ray computer tomography is increasingly growing in importance in quality assurance. The challenge is, on the one hand, to reliably recognize material faults, such as, for example, pores or cracks. On the other hand, the dimensional measuring of components is of great importance. This measuring of components to check whether the required manufacturing tolerances are adhered to is, however, difficult. Although, in principle, the distance between two selected points, for example to determine the position of an interior structure in the component, can be determined from the volume data record of the component to be investigated, which is determined by means of X-ray computer tomography, this distance determination is made more difficult by interfering effects, such as, for example, noise, scattered radiation or beam hardening, as these interfering effects change or falsify the grey values of the voxels in the volume data record. Moreover, grey value smears, which make a dimensional measurement of the component more difficult, occur in the transition between two different media, such as, for example, the object material and the air located in an interior cavity.